Problem: Solve for $x$ and $y$ using elimination. ${4x+y = 32}$ ${-3x-y = -26}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {4x+y = 32}\thinspace$ to find $y$ ${4}{(6)}{ + y = 32}$ $24+y = 32$ $24{-24} + y = 32{-24}$ ${y = 8}$ You can also plug ${x = 6}$ into $\thinspace {-3x-y = -26}\thinspace$ and get the same answer for $y$ : ${-3}{(6)}{ - y = -26}$ ${y = 8}$